Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(a(), a()) -> g(d())
, b() -> f(a(), a())
, g(a()) -> g(b())}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
The problem is match-bounded by 3.
The enriched problem is compatible with the following automaton:
{ a_0() -> 1
, a_1() -> 7
, a_1() -> 8
, a_2() -> 11
, a_2() -> 12
, g_0(1) -> 2
, g_0(2) -> 2
, g_0(3) -> 2
, g_0(4) -> 2
, g_0(5) -> 2
, g_1(6) -> 4
, g_1(9) -> 2
, g_2(10) -> 3
, g_3(13) -> 9
, b_0() -> 3
, b_1() -> 9
, f_0(1, 1) -> 4
, f_0(1, 2) -> 4
, f_0(1, 3) -> 4
, f_0(1, 4) -> 4
, f_0(1, 5) -> 4
, f_0(2, 1) -> 4
, f_0(2, 2) -> 4
, f_0(2, 3) -> 4
, f_0(2, 4) -> 4
, f_0(2, 5) -> 4
, f_0(3, 1) -> 4
, f_0(3, 2) -> 4
, f_0(3, 3) -> 4
, f_0(3, 4) -> 4
, f_0(3, 5) -> 4
, f_0(4, 1) -> 4
, f_0(4, 2) -> 4
, f_0(4, 3) -> 4
, f_0(4, 4) -> 4
, f_0(4, 5) -> 4
, f_0(5, 1) -> 4
, f_0(5, 2) -> 4
, f_0(5, 3) -> 4
, f_0(5, 4) -> 4
, f_0(5, 5) -> 4
, f_1(7, 8) -> 3
, f_2(11, 12) -> 9
, d_0() -> 5
, d_1() -> 6
, d_2() -> 10
, d_3() -> 13}
Hurray, we answered YES(?,O(n^1))Tool CDI
stdout:
MAYBE
Statistics:
Number of monomials: 149
Last formula building started for bound 3
Last SAT solving started for bound 3Tool EDA
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ f(a(), a()) -> g(d())
, b() -> f(a(), a())
, g(a()) -> g(b())}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^2))
Proof:
We have the following EDA-non-satisfying matrix interpretation:
Interpretation Functions:
a() = [0]
[2]
g(x1) = [1 2] x1 + [0]
[0 0] [0]
b() = [2]
[0]
f(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
[0 0] [0 0] [0]
d() = [0]
[0]
Hurray, we answered YES(?,O(n^2))Tool IDA
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(a(), a()) -> g(d())
, b() -> f(a(), a())
, g(a()) -> g(b())}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
Interpretation Functions:
a() = [0]
[3]
g(x1) = [1 3] x1 + [0]
[0 0] [0]
b() = [2]
[0]
f(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
[0 0] [0 0] [0]
d() = [0]
[0]
Hurray, we answered YES(?,O(n^1))Tool TRI
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(a(), a()) -> g(d())
, b() -> f(a(), a())
, g(a()) -> g(b())}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
a() = [0]
[3]
g(x1) = [1 3] x1 + [0]
[0 0] [0]
b() = [2]
[0]
f(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
[0 0] [0 0] [0]
d() = [0]
[0]
Hurray, we answered YES(?,O(n^1))Tool TRI2
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(a(), a()) -> g(d())
, b() -> f(a(), a())
, g(a()) -> g(b())}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
We have the following triangular matrix interpretation:
Interpretation Functions:
a() = [0]
[3]
g(x1) = [1 3] x1 + [0]
[0 0] [0]
b() = [2]
[0]
f(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
[0 0] [0 0] [0]
d() = [0]
[0]
Hurray, we answered YES(?,O(n^1))